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Assume that the H2 molecule behaves like a harmonic oscillator with a force constant k = 573 N/m the vibrational quantum number, corresponding to its dissociation energy 4.5 eV, is
- a)n = 6
- b)n = 7
- c)n = 8
- d)n = 15
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Assume that the H2 molecule behaves like a harmonic oscillator with a ...
For H2, the reduced mass (μ) 
Therefore, frequency of oscillation of the molecule is given by
For vibrational quantum number (n) corresponding to dissociation energy (Ediss), we have
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⇒
⇒
Therefore, frequency of oscillation of the molecule is given by
For vibrational quantum number (n) corresponding to dissociation energy (Ediss), we have
⇒
⇒
⇒
Most Upvoted Answer
Assume that the H2 molecule behaves like a harmonic oscillator with a ...
Given information:
- Force constant k = 573 N/m
- Dissociation energy = 4.5 eV
We can use the formula for the vibrational energy levels of a harmonic oscillator:
E = (n + 1/2)hν
where:
- E is the vibrational energy level
- n is the vibrational quantum number
- h is Planck's constant
- ν is the vibrational frequency
To find the vibrational frequency, we can use the formula:
ν = 1/2π * √(k/m)
where m is the reduced mass of the H2 molecule, which is half the mass of a single H atom:
m = 1/2 * m(H) = 1/2 * 1.00794 u = 0.50397 u
where u is the atomic mass unit.
Thus, the vibrational frequency is:
ν = 1/2π * √(573 N/m / (0.50397 u * 1.66054 x 10^-27 kg/u)) = 1.041 x 10^14 Hz
To find the vibrational quantum number corresponding to a dissociation energy of 4.5 eV, we can use the formula:
E(n) - E(n-1) = hν
where E(n) and E(n-1) are the energies of two adjacent vibrational levels.
Solving for n, we get:
n = (E(dissociation) / hν) + 1/2
where E(dissociation) is the dissociation energy in joules.
Converting 4.5 eV to joules:
E(dissociation) = 4.5 eV * 1.60218 x 10^-19 J/eV = 7.21581 x 10^-19 J
Substituting the values:
n = (7.21581 x 10^-19 J / (6.62607 x 10^-34 J s * 1.041 x 10^14 Hz)) + 1/2 = 8.06
Rounding to the nearest integer, we get n = 8, which is the correct answer (option C).
- Force constant k = 573 N/m
- Dissociation energy = 4.5 eV
We can use the formula for the vibrational energy levels of a harmonic oscillator:
E = (n + 1/2)hν
where:
- E is the vibrational energy level
- n is the vibrational quantum number
- h is Planck's constant
- ν is the vibrational frequency
To find the vibrational frequency, we can use the formula:
ν = 1/2π * √(k/m)
where m is the reduced mass of the H2 molecule, which is half the mass of a single H atom:
m = 1/2 * m(H) = 1/2 * 1.00794 u = 0.50397 u
where u is the atomic mass unit.
Thus, the vibrational frequency is:
ν = 1/2π * √(573 N/m / (0.50397 u * 1.66054 x 10^-27 kg/u)) = 1.041 x 10^14 Hz
To find the vibrational quantum number corresponding to a dissociation energy of 4.5 eV, we can use the formula:
E(n) - E(n-1) = hν
where E(n) and E(n-1) are the energies of two adjacent vibrational levels.
Solving for n, we get:
n = (E(dissociation) / hν) + 1/2
where E(dissociation) is the dissociation energy in joules.
Converting 4.5 eV to joules:
E(dissociation) = 4.5 eV * 1.60218 x 10^-19 J/eV = 7.21581 x 10^-19 J
Substituting the values:
n = (7.21581 x 10^-19 J / (6.62607 x 10^-34 J s * 1.041 x 10^14 Hz)) + 1/2 = 8.06
Rounding to the nearest integer, we get n = 8, which is the correct answer (option C).
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Assume that the H2 molecule behaves like a harmonic oscillator with a force constant k = 573 N/m the vibrational quantum number, corresponding to its dissociation energy 4.5 eV,isa)n = 6b)n = 7c)n = 8d)n = 15Correct answer is option 'C'. Can you explain this answer?
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Assume that the H2 molecule behaves like a harmonic oscillator with a force constant k = 573 N/m the vibrational quantum number, corresponding to its dissociation energy 4.5 eV,isa)n = 6b)n = 7c)n = 8d)n = 15Correct answer is option 'C'. Can you explain this answer? for GATE 2025 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Assume that the H2 molecule behaves like a harmonic oscillator with a force constant k = 573 N/m the vibrational quantum number, corresponding to its dissociation energy 4.5 eV,isa)n = 6b)n = 7c)n = 8d)n = 15Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Assume that the H2 molecule behaves like a harmonic oscillator with a force constant k = 573 N/m the vibrational quantum number, corresponding to its dissociation energy 4.5 eV,isa)n = 6b)n = 7c)n = 8d)n = 15Correct answer is option 'C'. Can you explain this answer?.
Assume that the H2 molecule behaves like a harmonic oscillator with a force constant k = 573 N/m the vibrational quantum number, corresponding to its dissociation energy 4.5 eV,isa)n = 6b)n = 7c)n = 8d)n = 15Correct answer is option 'C'. Can you explain this answer? for GATE 2025 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Assume that the H2 molecule behaves like a harmonic oscillator with a force constant k = 573 N/m the vibrational quantum number, corresponding to its dissociation energy 4.5 eV,isa)n = 6b)n = 7c)n = 8d)n = 15Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Assume that the H2 molecule behaves like a harmonic oscillator with a force constant k = 573 N/m the vibrational quantum number, corresponding to its dissociation energy 4.5 eV,isa)n = 6b)n = 7c)n = 8d)n = 15Correct answer is option 'C'. Can you explain this answer?.
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Assume that the H2 molecule behaves like a harmonic oscillator with a force constant k = 573 N/m the vibrational quantum number, corresponding to its dissociation energy 4.5 eV,isa)n = 6b)n = 7c)n = 8d)n = 15Correct answer is option 'C'. Can you explain this answer?, a detailed solution for Assume that the H2 molecule behaves like a harmonic oscillator with a force constant k = 573 N/m the vibrational quantum number, corresponding to its dissociation energy 4.5 eV,isa)n = 6b)n = 7c)n = 8d)n = 15Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of Assume that the H2 molecule behaves like a harmonic oscillator with a force constant k = 573 N/m the vibrational quantum number, corresponding to its dissociation energy 4.5 eV,isa)n = 6b)n = 7c)n = 8d)n = 15Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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